Related papers: Spontaneous stochasticity and renormalization grou…
Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single…
This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…
The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our intention is to extend the periodic unfolding method to the…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a…
This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that…
This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditional models usually assume constant-intensity noise, but many…
We study a self-organized critical system under influence of turbulent motion of the environment. The system is described by the anisotropic continuous stochastic equation proposed by Hwa and Kardar [{\it Phys. Rev. Lett.} {\bf 62}: 1813…
Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The stirring and mixing are modelled by a random…
In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…
Metastability in open system dynamics describes the phenomena of initial relaxation to longlived metastable states before decaying to the asymptotic stable states. It has been predicted in continuous-time stochastic dynamics of both…
The field theoretic renormalization group and the operator product expansion are applied to the model of passive vector (magnetic) field advected by a random turbulent velocity field. The latter is governed by the Navier--Stokes equation…
Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not…
Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is…
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations…
In this paper we study the vanishing inertia and viscosity limit of a second order system set in an Euclidean space, driven by a possibly nonconvex time-dependent potential satisfying very general assumptions. By means of a variational…
We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…